The submodularity ratio was first introduced to analyze the forward regression and orthogonal matching pursuit algorithms for linear regression [1]}. It was latter related to restricted strong convexity [2]}, leading to similar guarantees for generalized linear model (GLM) likelihood, graphical model learning objectives, or an arbitrary M-estimator. The strength of the submodularity ratio is that for all applications it suffices to estimate the value of \(\gamma \)  to obtain guarantees for greedy algorithms even in other modes of computation [3]}, [4]}. This has lead to new guarantees for sensor placement problems [5]}, experimental design [6]}, [7]} and low rank optimization [8]}. Weak submodularity and related algorithmic techniques have also been used for document summarization [9]} and interpretation of neural networks [4]}.
